Practice Final Exam
Problem 1
Determine the currents i and i1 using only Simple Circuit Methods.
Problem 2
Determine the voltage across the 3k resistor for the circuit shown using only Node
Analysis.
Problem 3
Determine the voltage vbc across the 20 resistor using Mesh Analysis.
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Problem 4
Find the Thévenin equivalent circuit for the circuit shown.
Problem 5
Find the voltage v0 and the current i0 when the Op Amp is assumed to be ideal.
Problem 6
The input to the circuit is iS(t) = 2 + 4u(t) A.
a. Determine the voltage v(t) across the left-handed 3 resistor for t > 0.
b. Plot and fully label v(t) and interpret the result.
Problem 7
Find the complete response of the capacitor v(t) for t > 0 for the circuit. Assume the
circuit is at steady state at t = 0.
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Problem 8
Determine the steady-state voltage across the capacitor using Simple Circuit Techniques.
Problem 9
Determine the node Phasor voltages at terminals a and b for the circuit using Mesh
Analysis when VS = j50 V and V1 = j30 V.
Problem 10
Determine the Thévenin equivalent at the output terminals a–b with a signal vS =
cos(10,000t + 53.10).
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Exam 1 Equation Sheet
v S  ReqiS
R
 in  0
in  RP iS
n
 vn  0
R
v n  Rn v S
S
v n2 2
Pn  v nin 
 inRn
Rn
 Sum of conductances 
 Mutual conductances
  v1  

 attached to node 1

   v 2 ,v 3 ,

 Sum of resistors 
  vSources
Node Analysis:  attached to node 1
 Mutual resistors 
i 
 i ,i ,
Mesh Analysis:  attached to loop 1 1  attached to loop 1  2 3
  iSources
Number of loops/nodes – Number of sources
= Number of loop/node equations
+ Number of Superloop/Supernode Conditions
+ Number of Dependent Source Conditions
Total number of equations that must be solved
Thévenin’s Theorem:
RTh 
v OC
iSC
Ideal Op Amp Model: i1 = i2 = 0 and v1 = v2
Exam 2 Equation Sheet
First Order Circuits
Constant Sources
RC-Circuit:
v C (t)  VOC  [v c (0 )  VOC ]e t /  where   RThCeq and VOC  v Th
RL-Circuit:
iL (t)  ISC  [iL (0 )  ISC ]e t /  where   L eq /RTh and ISC  iN
Second Order Circuits
Step 1: Use KVL, KCL, vL = LdiL/dt, and iC = CdvC/dt to obtain two first order response
equations that are functions of vC and iL. Solve for the 2nd order equation.
Step 2: Set the effective source equal to zero and obtain the characteristic equation;
then solve for the characteristic roots.
s2  2s  02  0  s1,s2    2  02
Step 3: From the values of  and o, determine the type of natural response of the
circuit.

 = o → Critically Damped: xcritical (t)  et (A1t  A 2 )

 > o → Overdamped: xover (t)  A1es1t  A 2es2 t

 < o → Underdamped:
xunder (t)  et (A1 cos dt  A 2 sin dt), where d  02  2
Step 4: For a constant source, xf(t) = B. Substitute this into the 2nd order equation and
determine the constant B. Write out the complete response:
x(t)  A1xn1  A 2xn2  B
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Step 5: Find the numerical value for the initial conditions vC(0+ ), iL(0+ ) and dx2(0+ )/dt. Use
equations (1) & (2) in Step 1 to numerically solve for the derivative dx2(0+)/dt after the
switch has been thrown.
Step 6: Apply the initial conditions to the general response and determine A1 and A2.
 Setup up two equations involving x2(0+) and dx2(0+)/dt and solve for A1 and A2
 Write down the complete response for the circuit.
Step 7: Solve the circuit problem and interpret





a1 b1   x   c1 
   

a2 b2   y   c 2 
c 1 b1
 x 
c 2 b2
D2
e jθ  cosθ  jsinθ
a1
c1
a2 c 2
D2
and y 
xe  Be j(ωt )
XC 
1
C
D2 
a1
b1
a2
b2
 a1b 2  b1a 2
x(t)  Re{x e }  Bcos(ωt  )
x(t)  Xm cos(ωt  )  Re{Xme j(ωt ) }
  2πf
where
X  Xme j  Xm
XL  L
 Z 
Z  R2  X2
 j
V

Z =  Ze
where 
1 X
I
R  jX
  tan

R

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